Calculators for determining the F or P value of a thermal process

The Dairy Science and Food Technology website contains several free, On Line calculators, for determining the cumulative lethality (F, B*, P or PU) of thermal processes, the concentration of Thermal Process Indicators (TTI) following UHT treatment of milk and several other process indicators.

These calculators are listed on the Calculators and Models page under Thermal Processing e.g.

• Calculator for determining the lethality (F, value) of a thermal process using the Trapezoid and Simpson's rules. This unique calculator works with thousands of pasted values e.g. from a data logger.
• Calculator for determining the lethality (F, B* values) and chemical changes (C* value, formation of HMF, Lactulose, Furosine, and destruction of thiamine) in heated milk integrated using the Trapezoid and Simpson's rules.
• Calculator for determining the lethality (F, B* values) and chemical changes (C* value) for generic high-temperature processes using the Trapezoid and Simpson's rules. 
• Determine the accuracy of 3 algorithms for predicting the concentration of lactulose in milk after defined heat treatment.

The lethality calculators convert temperature readings to lethal rates, plot the lethal rates against time, and determine appropriate lethality values or chemical indicators for a heat process whether using hot water, saturated steam or dry heat. The area under the time-lethality curve is determined by numerical integration using the industry standard method, the trapezoid rule or the more accurate Simpson's rules or both for comparative purposes. In general, the more values, the more accurate the value for F or P will be. One of the calculators will also upload CSV files of a thermal process and provides a facility for free, independent validation of a thermal process.

The lethal effect of high temperatures on microorganisms is dependent on several factors, including temperature, holding time, pH and water activity. Note fat, sugar, salt and chocolate content have a major effect on the sensitivity of microorganisms to heat; in general they markedly increase their resistance to heat e.g. salmonella can survive several hours at high temperatures in molten chocolate.

Because microorganisms in foods are exposed to lethal temperatures as they reach the target processing temperature, during holding and during cooling, it is necessary to calculate the cumulative effect of heat on microbial destruction during both heating and cooling as well at the holding time at the target temperature to obtain a true estimate of the lethal effects of a heat treatment process.

The logarithmic reduction in time required to kill the same number of microorganisms as the temperature is increased has been well described.  This can be expressed by calculating lethal rate.

The lethal rate is a dimensionless number and can be calculated using equation 1 (Stobo, 1973) and is a relative term that compares the microbial killing effect at a measured temperature to one minute at the reference temperature.

Equation 1, Lethal rate = 10 ^(T-Tr)/z  where T is the temperature, in Celsius, at which the lethal rate is calculated and Tr is the reference temperature at which the equivalent lethal effect is compared. The z-value measured in °C is the reciprocal of the slope of the thermal death curve for the target microorganism or spore; 10° C is the value frequently used in F_o calculations performed on low-acid foods.

Use of this equation can be illustrated using the following example. Calculate the lethal rate at 110° C compared to that at 121.11° C (Tr), given that the most heat-resistant organism present has a Z value of 10° C.

Lethal rate= 10 ^{(110-121.11)/10}

 = 0.077.

Lethal rates when plotted against process time can be used to calculate the F or P value of a thermal process.  The F or P value can be defined as the time or equivalent time taken to reduce initial microbial numbers, at a specified temperature, by a particular value, normally a multiple of the D-value for the target organism. P or PU values are often used to designate pasteurization-type heat treatments that typically give 6-log reductions of target organisms, whereas F values are often used to designate much higher heat treatment processes giving higher log reductions. F and P are used interchangeably throughout this website.

Note the original work on thermobacteriology used a reference temperature of 250° F. This is equivalent to 121.1°C.

Tr will vary depending on whether F₀ is being calculated or whether a pasteurisation process or other heat treatment e.g. a sous vide process being assessed. A Tr value of 121.1° C is used in the determination of F₀. If F₇₀ or another F value is required, then Tr can be set at 70° C or other temperature.

Tr can be varied by the user. The default  Z-value has been set at 10° C and can be varied by the user in this application.  Note that the Z-value has a significant effect on F value, refer to the free download of lethality tables formulated using Z-values of 6°,8°,10° and 12°C. 

There is also a facility to perform a lethality calculation using an uploaded CSV file. Basic instructions are provided in the help file. The application can be tested using internal data and you can also upload a data file for analysis of a process.

The calculators can also be used to calculate dry heat sterilisation (F_H) and dry heat depyrogenation (F_D) values providing the correct Tr and Z values are used.

Spreadsheets for undertaking thermal processing calculations can be downloaded, some are also available for free download.

 
How to cite this article

Mullan, W.M.A. (2007). [On-line]. Available from: https://www.dairyscience.info/index.php/thermal-processing/134-f-value-thermal-process.html?tmpl=component&print=1&layout=default&page= . Accessed: 19 April, 2024. Updated 2014, 2015, 2016, 2017, 2018. 

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